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The main steps are summarized in the following equation: [6] 3 ⁄ 4 Li 2 CO 3 + 3 ⁄ 2 GeO 2 + 3 NH 4 H 2 PO 4 + 1 ⁄ 4 Al 2 O 3 → Li 1.5 Al 0.5 Ge 1.5 (PO 4) 3 + 3 NH 3 + 3 ⁄ 4 CO 2 + 9 ⁄ 2 H 2 O. The annealing temperature is selected to promote the full crystallization and avoiding the formation of detrimental secondary phases, pores ...
Simulations establish the number of steps to convergence. For the moving truck example described above, with Δ t = 1 {\displaystyle \Delta t=1} . and σ a 2 = σ z 2 = σ x 2 = σ x ˙ 2 = 1 {\displaystyle \sigma _{a}^{2}=\sigma _{z}^{2}=\sigma _{x}^{2}=\sigma _{\dot {x}}^{2}=1} , simulation shows convergence in 10 {\displaystyle 10} iterations.
The number of points on the projective line and projective space are so easy to calculate because they can be written as disjoint unions of a finite number of copies of affine spaces. It is also easy to prove the Weil conjectures for other spaces, such as Grassmannians and flag varieties, which have the same "paving" property.
In Arithmetica, Diophantus is the first to use symbols for unknown numbers as well as abbreviations for powers of numbers, relationships, and operations; [41] thus he used what is now known as syncopated algebra. The main difference between Diophantine syncopated algebra and modern algebraic notation is that the former lacked special symbols ...
The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size = in terms of N 1 smaller DFTs of sizes N 2, recursively, to reduce the computation time to O(N log N) for highly composite N (smooth numbers).
The first symbol of an alternative may be the class being defined, the repetition, as explained by Naur, having the function of specifying that the alternative sequence can recursively begin with a previous alternative and can be repeated any number of times. [2] For example, above <expr> is defined as a <term> followed by any number of <addop ...
The total number of seats has been reduced and regional lists have been eliminated. The number of single-member seats has increased from 45.56% of the total to 53.3%. The first ballot is to choose MPs for 106 single-member districts using first-past-the-post.